Sumários
Distributions of some important continuous random variables
26 Abril 2016, 11:00 • Graça Leão Fernandes
Distributions of some important continuous random variables:
- Normal distribution:
- aditivity theorem - the cases when the mean and variance are different \ equal for each of the parcel variables;
- examples.
- Exponential distribution:
- association with the Poisson Process;
- definition;
- probability density and cumulative distribution functions;
- computing probabilities
- the lack of memory property
Some important distribution of continuous random variables
21 Abril 2016, 10:30 • Graça Leão Fernandes
Some important distribution of continuous random variables:
- Uniforme continuous in the interval (alfa, beta):
- definition;
- density and cumulative distribution functions;
- moment generating function - mean, variance and assimetry coeficient.
- the particular case of the Uniforme (0,1):
- probability integer transformation;
- examples.
- Normal distribution:
- reasons why it is so important;
- definition;
- density and cumulative distribution functions;
- moment generating function - mean, variance and assimetry coeficient;
- standardization process - the normal standard.
- definition;
- density and cumulative distribution functions;
- using tables and calculator to compute probabilities;
- how to use the tables and the calculator to find values for the inverse c.d.f.;
- examples.
Some important distributions of discrete random variables.
19 Abril 2016, 11:00 • Graça Leão Fernandes
Some important distributions of discrete random variables:
- Poisson distribution:
- Poisson process and its assumptions;
- definition;
- probability and cumulative distribution functions;
- moment generating function, mean and variance;
- using tables and calculator to compute probabilities;
- aditivity theorem;
- Law of rare events.
Some important discrete random variables distributions
14 Abril 2016, 10:30 • Graça Leão Fernandes
Some important discrete random variables distributions
- uniform discrete:
- definition;
- probability and cumulative distribution functions;
-moment generating function and some moments(mean, variance)
- Bernoulli:
- definition of a Bernoulli trial;
- probability function;
-moment generating function and some moments(mean, variance)
- independent Bernoulli trials.
- Binomial
- distribution of the sum of independent variables followng a Bernoulli distribution;
- probability and distribution functions;
-moment generating function and some moments(mean, variance);
- computing probabilities using the tables and the calculator;
- aditivity theorem.
Two dimensional random variables: Correlation coeficient, marginal expected values and variances, conditional expectations
12 Abril 2016, 11:00 • Graça Leão Fernandes
Two dimensional random variables:
- Correlation coeficient:
- definition, interpretation;
- correlation and independence.
- marginal expected values and variances.
- conditional expectations.